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Inhalt des Dokuments

Absolventen-Seminar • Numerische Mathematik

Absolventen-Seminar
Verantwortliche Dozenten:
Prof. Dr. Christian MehlProf. Dr. Volker Mehrmann
Koordination:
Benjamin Unger, Dr. Matthias Voigt
Termine:
Do 10:00-12:00 in MA 376
Inhalt:
Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen
Sommersemester 2018 Vorläufige Terminplanung
Datum
Zeit
Raum
Vortragende(r)
Titel
Do 19.04.
10:15
Uhr
MA 376
Vorbesprechung
Do 26.04.
10:15
Uhr
MA 376
Yue Wu
Randomized numerical schemes for (S)ODEs/SPDEs [abstract]
Matthias Voigt
Do 03.05.
10:15 Uhr
MA 376
no seminar
Do 10.05.
10:15
Uhr
MA 376
no seminar
Do 17.05.
10:15
Uhr
MA 376
Benjamin Pehersdorfer
Murat Manguoglu
Do
24.05.
10:15
Uhr
MA 376
Christian Mehl
Candan Güdücü
Do
31.05.
10:15
Uhr
MA 376
Robert Altmann
Christoph Zimmer
Do 07.06.
10:15
Uhr
MA 376
Jeroen Stolwijk
Ines Ahrens
Do 14.06.
10:15
Uhr
MA 376
Daniel Bankmann
Riccardo Morandin
Do 21.06.
10:15
Uhr
MA 376
Heinrich Ellmann
Jesse Scherwitz
Do 28.06.
10:15
Uhr
MA 376
Volker Mehrmann
Do 05.07.
10:15 Uhr
MA 376
Felix Black
Pia Lutum
Do 12.07.
10:15
Uhr
MA 376
Marine Froidevaux
Sofia Bikopoulou
Do 19.07.
10:15
Uhr
MA 376
Arbi Moses Badlyan
Philipp Schulze

 

 

Abstracts zu den Vorträgen:

Yue Wue (TU Berlin)

Donnerstag, 26. April 2018

Randomized numerical schemes for (S)ODEs/SPDEs

A wide range of applications, for instance, in the engineering and physical sciences as well as in computational finance is still spurring the demand for the development of more efficient algorithms and their theoretical justification. In particular, the current focus lies on the approximation of ODEs/S(P)DEs which cannot be treated by standard methods found in textbook.

We, therefore, first developed two randomized explicit Runge–Kutta schemes for ordinary differential equations (ODEs) with time-irregular coeffcient functions. In particular, the methods are applicable to ODEs of Carathéodory type, whose coeffcient functions are only integrable with respect to the time variable but are not assumed to be continuous. An important ingredient in the analysis are corresponding error bounds for the randomized Riemann sum quadrature rule.

It is demanding to approximate numerical solutions of non-autonomous SDEs where the standard smoothness and growth requirements of standard Milstein-type methods are not fulfilled. In the case of a non-differentiable drift coefficient function f, we proposed a drift-randomized Milstein method to achieve a higher order approximation and discussed the optimality of our convergence rates.

We also pushed the idea to the numerical solution of non-autonomous semilinear stochastic evolution equations (SEEs) driven by an additive Wiener noise. Usually quite restrictive smoothness requirements are imposed in order to achieve high order of convergence rate. It turns out that the resulting method converges with a higher rate with respect to the temporal discretization parameter without requiring any differentiability of the nonlinearity. Our approach also relaxes the smoothness requirements of the coefficients with respect to the time variable considerably.

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